Question

\(\left\{{}\begin{matrix}\frac{1}{x-3}+\frac{1}{y-4}=1\\\frac{x+1}{x-3}+\frac{y-2}{y-4}=5\end{matrix}\right.\)

Giải hệ phương trình

Answer 1

ĐKXĐ:...

Đặt \(\frac{1}{x-3}=m\Rightarrow\frac{1}{m}=x-3\Leftrightarrow x+1=\frac{1}{m}+4\)

\(\frac{1}{y-4}=n\Rightarrow\frac{1}{n}=y-4\Leftrightarrow y-2=\frac{1}{n}+2\)

\(\Rightarrow\left\{{}\begin{matrix}m+n=1\\\left(\frac{1}{m}+4\right).m+\left(\frac{1}{n}+2\right).n=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m+n=1\\4m+2n+2=5\end{matrix}\right.\)

Giải nốt nhé :)